Scattering from an elastic shell and a rough fluid-elastic interface: Theory

Journal of the Acoustical Society of America

Volumn 101, Issue 2, 1997, Pages 767-788

  Bishop, Garner C ^a   Smith, Judy ^a  

^a NAVAL UNDERSEA WARFARE CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; INTERFACES (MATERIALS); PRESSURE; SURFACE ROUGHNESS; TENSORS; WAVEGUIDES;

ELASTIC SHELL; HELMHOLTZ-KIRCHHOFF INTEGRALS; NULL FIELD T MATRIX METHOD; SPHERICAL BASIS FUNCTION; WEYL PLANE WAVES;

ACOUSTIC WAVE SCATTERING;

ACOUSTICS; ARTICLE; ELASTICITY; GEOMETRY; LIQUID; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; SOUND TRANSMISSION; THEORY;

EID: 0031081623     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.417962     Document Type: Article

References (28)

1. G. Kristensson and S. Strom, "Scattering from buried inhomogeneities - a general three-dimensional formalism," J. Acoust. Soc. Am. 64, 917-936 (1978).
2. G. Kristensson and S. Strom, "The T-matrix approach to scattering from buried inhomogeneities," in Acoustic, Electromagnetic and Elastic Wave Scattering-Focus on the T-matrix Approach, edited by V. K. Varadan and V. V. Varadan (Pergamon, New York, 1980), pp. 135-167.
3. R. H. Hackman and G. S. Sammelmann, "Acoustic scattering in an inhomogeneous waveguide: Theory," J. Acoust. Soc. Am. 80, 1447-1458 (1986).
4. G. S. Sammelmann and R. H. Hackman, "Acoustic scattering in a homogeneous waveguide," J. Acoust. Soc. Am. 82, 324-336 (1987).
5. R. H. Hackman and G. S. Sammelmann, "Long-range scattering in a deep oceanic waveguide," J. Acoust. Soc. Am. 83, 1776-1793 (1988).
6. R. H. Hackman and G. S. Sammelmann, "Multiple scattering analysis for a target in an oceanic waveguide," J. Acoust. Soc. Am. 84, 1813-1825 (1988).
7. G. C. Bishop and J. Smith, "A T-matrix for scattering from a doubly infinite fluid-solid interface with doubly periodic surface roughness," J. Acoust. Soc. Am. 94, 1560-1583 (1993).
8. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 7.
9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 13.
10. Y. Pao and V. Varatharajulu, "Huygens' principle, radiation conditions, and integral formulas for the scattering of elastic waves," J. Acoust. Soc. Am. 59, 1361-1371 (1976).
11. P. C. Waterman, "Matrix theory of elastic wave scattering," J. Acoust. Soc. Am. 60, 567-580 (1976).
12. A. Bostrom, "Scattering of stationary acoustic waves by an elastic obstacle immersed in a fluid," J. Acoust. Soc. Am. 67, 390-398 (1980).
13. The spherical scalar basis functions defined in Eq. (10) are identical to those defined by Hackmann and Sammelmann in Ref. 3, however, they differ from those defined by Morse and Feshbach in Ref. 9 who do not define orthonormal scalar spherical harmonics.
14. The spherical vector harmonics defined in Eq. (13) are identical to those defined by Hackmann and Sammelmann in Ref. 5 and Bostrom in Ref. 12, but differ from those defined by Morse and Feshbach in Ref. 9 and Waterman in Ref. 11 who obtain the vector spherical harmonics from spherical scalar harmonics in the same manner given in Eq. (13), but who do not use orthonormal spherical scalar harmonics.
15. The vector spherical basis functions defined here, are a generalization of those defined by Bostrom in Ref. 12 in that both regular and irregular vector spherical basis functions are defined, and are normalized differently than the vector spherical basis functions defined by Morse and Feshbach in Ref. 9, Waterman in Ref. 11, and Pao and Varatharajulu in Ref. 10 all of whom use different normalizations.
16. 0(r,r′;k) used in this paper includes an additional factor of 1/4π. The Green function defined by Bostrom in Ref. 12 satisfies the equation (∇2+k2)g0(r,r′;k) = -(1/k)δ(r-r′).
17. A. Bostrom, "Scattering of acoustic waves by a layered elastic object in a fluid-An improved null field approach," J. Acoust. Soc. Am. 76, 588-593 (1984).
18. s)δ(r-r′)I. This form of the Green dyadic is also used by Bostrom in Ref. 12.
19. E. Mertzbacher, Quantum Mechanics (Wiley, New York, 1970), 2nd ed., pp. 299-301.
20. D. K. Dacol and D. H. Berman, "Sound scattering from a randomly rough fluid-solid interface," J. Acoust. Soc. Am. 84, 292-302 (1988).
21. M. Nieto-Vesperinas and N. Garcia, "A detailed study of the scattering of scalar waves from random rough surfaces," Opt. Acta 28, 1651-1672 (1981).
22. D. R. Jackson, D. P. Winebrenner, and A. Ishimaru, "Comparison of perturbation theories for rough-surface scattering," J. Acoust. Soc. Am. 83, 961-969 (1988).
23. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1980), 2nd ed., p. 43.
24. J. A. Hudson, The Excitation and Propagation of Elastic Waves (Cambridge U.P., Cambridge, England, 1987), pp. 67-71.
25. A. G. Voronovich, "Small slope approximation in wave scattering by rough surfaces," Sov. Phys. JETP 62, 65-70 (1985).
26. D. H. Berman, "Simulations of rough surface scattering," J. Acoust. Soc. Am. 89, 623-636 (1991).
27. T. Yang and S. L. Broschat, "Acoustic scattering from a fluid-elastic-solid interface using the small slope approximation," J. Acoust. Soc. Am. 96, 1796-1804 (1994).
28. Reference 9, p. 117.